Abstract
In this work, we use the angular diameter distances of 38 galaxy clusters with joint X-ray/SZE observation to circumvent the circularity problem in the Amati relation for Gamma-ray Bursts (GRBs). Assuming the validity of cosmic-distance duality relation, we obtain the luminosity distance from the cluster angular diameter distance and use that to calculate the isotropic equivalent energy of two different GRB datasets, after restricting the GRB redshift range to z < 0.9. We then use these GRB datasets to test the Amati relation at the low redshifts using the galaxy cluster distances. Our best-fit Amati relation parameters are consistent with a previous estimate for the same dataset. The intrinsic scatter which we obtain for the two datasets is about 45% and 15%, and is comparable with that found by other distance anchors used to study the Amati relation.
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